Changing Apple ID Notification Email address
I'm at https://appleid.apple.com/account/manage/section/security and when I click on Notification Email to change it, it asks me for the new email, which is different from my Apple ID email, but once I do, it then states I must go to another device, navigate to Settings > Apple ID and continue. Continue what? I've tried this on my Mac and my iPhone, and nothing allows me to actually do anything to change the ID. I get no email saying it's been done...I just keep trying and keep getting the same message, but with no instructions.
The notification email listed is an old employer, and I DO NOT want them to get my notifications!! Please help get me through the WHOLE process. I'm stuck in an endless loop. Thanks.
iMac 27″, macOS 10.13